The Law of One Price
To understand the market forces that might give rise to the results predicted by the purchasing
power parity theory, we discuss first a related but distinct proposition known as the law
of one price. The law of one price states that in competitive markets free of transportation
costs and official barriers to trade (such as tariffs), identical goods sold in different countries
must sell for the same price when their prices are expressed in terms of the same
currency. For example, if the dollar/pound exchange rate is per pound, a sweater that
sells for in New York must sell for £30 in London. The dollar price of the sweater
when sold in London is then ($1.50 per pound) × (£30 per sweater) = $45 per sweater, the
same as its price in New York.
Let’s continue with this example to see why the law of one price must hold when trade
is free and there are no transport costs or other trade barriers. If the dollar/pound exchange
rate were per pound, you could buy a sweater in London by converting $43.50
(= $1.45 per pound × £30) into £30 in the foreign exchange market. Thus, the dollar price
of a sweater in London would be only . If the same sweater were selling for in
New York, U.S. importers and British exporters would have an incentive to buy sweaters
in London and ship them to New York, pushing the London price up and the New York
price down until prices were equal in the two locations. Similarly, at an exchange rate of
per pound, the dollar price of sweaters in London would be $46.50 (= $1.55 per
pound × £30), $1.50 more than in New York. Sweaters would be shipped from west to east
until a single price prevailed in the two markets.
The law of one price is a restatement, in terms of currencies, of a principle that was
important in the trade theory portion of this book: When trade is open and costless, identical
goods must trade at the same relative prices regardless of where they are sold. We
remind you of that principle here because it provides one link between the domestic prices
of goods and exchange rates. We can state the law of one price formally as follows: Let
be the dollar price of good when sold in the United States, the corresponding
euro price in Europe. Then the law of one price implies that the dollar price of good is the
same wherever it is sold.
PUS
i = 1E$/€2 * 1PE i 2.
i
PE i PUS i
i
$1.55
$43.50 $45
$1.45
$45
$1.50
386 PART THREE Exchange Rates and Open-Economy Macroeconomics
Equivalently, the dollar/euro exchange rate is the ratio of good ’s U.S. and European
money prices,
To understand the market forces that might give rise to the results predicted by the purchasing
power parity theory, we discuss first a related but distinct proposition known as the law
of one price. The law of one price states that in competitive markets free of transportation
costs and official barriers to trade (such as tariffs), identical goods sold in different countries
must sell for the same price when their prices are expressed in terms of the same
currency. For example, if the dollar/pound exchange rate is per pound, a sweater that
sells for in New York must sell for £30 in London. The dollar price of the sweater
when sold in London is then ($1.50 per pound) × (£30 per sweater) = $45 per sweater, the
same as its price in New York.
Let’s continue with this example to see why the law of one price must hold when trade
is free and there are no transport costs or other trade barriers. If the dollar/pound exchange
rate were per pound, you could buy a sweater in London by converting $43.50
(= $1.45 per pound × £30) into £30 in the foreign exchange market. Thus, the dollar price
of a sweater in London would be only . If the same sweater were selling for in
New York, U.S. importers and British exporters would have an incentive to buy sweaters
in London and ship them to New York, pushing the London price up and the New York
price down until prices were equal in the two locations. Similarly, at an exchange rate of
per pound, the dollar price of sweaters in London would be $46.50 (= $1.55 per
pound × £30), $1.50 more than in New York. Sweaters would be shipped from west to east
until a single price prevailed in the two markets.
The law of one price is a restatement, in terms of currencies, of a principle that was
important in the trade theory portion of this book: When trade is open and costless, identical
goods must trade at the same relative prices regardless of where they are sold. We
remind you of that principle here because it provides one link between the domestic prices
of goods and exchange rates. We can state the law of one price formally as follows: Let
be the dollar price of good when sold in the United States, the corresponding
euro price in Europe. Then the law of one price implies that the dollar price of good is the
same wherever it is sold.
PUS
i = 1E$/€2 * 1PE i 2.
i
PE i PUS i
i
$1.55
$43.50 $45
$1.45
$45
$1.50
386 PART THREE Exchange Rates and Open-Economy Macroeconomics
Equivalently, the dollar/euro exchange rate is the ratio of good ’s U.S. and European
money prices,
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